The equation of the ellipse centred at (1,2), one focus at (6,2) and passing through the point (4,6), is
A
(x−1)245+(y−2)220=1
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B
(x−1)25+(y−2)220=1
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C
(x−1)220+(y−2)245=1
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D
(x−2)220+(y−1)245=1
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Solution
The correct option is A(x−1)245+(y−2)220=1
Let S≡(6,2) and C≡(1,2) , slope of CS=0, therefore major axis of the ellipse is parallel to x−axis and minor axis is parallel to y−axis. As C is the mid point of both foci ∴ other focus S1≡(−4,2) We know that PS+PS1=2a 2√5+4√5=2a⇒a2=45
Now SS1=2ae=10 a2e2=25=a2−b2⇒b2=20
Hence equation of required ellipse is (x−1)245+(y−2)220=1